The Experts below are selected from a list of 202413 Experts worldwide ranked by ideXlab platform
Jean-christophe Mourrat - One of the best experts on this subject based on the ideXlab platform.
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An Iterative Method for elliptic problems with rapidly oscillating coefficients
ESAIM: Mathematical Modelling and Numerical Analysis, 2021Co-Authors: Scott Armstrong, Antti Hannukainen, Tuomo Kuusi, Jean-christophe MourratAbstract:We introduce a new Iterative Method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid Method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid Methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our Method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the Method, with openly available source code.
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An Iterative Method for elliptic problems with rapidly oscillating coefficients
2018Co-Authors: Scott Armstrong, Antti Hannukainen, Tuomo Kuusi, Jean-christophe MourratAbstract:We introduce a new Iterative Method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid Method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid Methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our Method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the Method.
Scott Armstrong - One of the best experts on this subject based on the ideXlab platform.
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An Iterative Method for elliptic problems with rapidly oscillating coefficients
ESAIM: Mathematical Modelling and Numerical Analysis, 2021Co-Authors: Scott Armstrong, Antti Hannukainen, Tuomo Kuusi, Jean-christophe MourratAbstract:We introduce a new Iterative Method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid Method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid Methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our Method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the Method, with openly available source code.
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An Iterative Method for elliptic problems with rapidly oscillating coefficients
2018Co-Authors: Scott Armstrong, Antti Hannukainen, Tuomo Kuusi, Jean-christophe MourratAbstract:We introduce a new Iterative Method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid Method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid Methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our Method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the Method.
Lothar Reichel - One of the best experts on this subject based on the ideXlab platform.
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an Iterative Method for tikhonov regularization with a general linear regularization operator
Journal of Integral Equations and Applications, 2010Co-Authors: Michiel E. Hochstenbach, Lothar ReichelAbstract:Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed problems with error-contaminated data. A regularization operator and a suitable value of a regularization parameter have to be chosen. This paper describes an Iterative Method, based on Golub-Kahan bidiagonalization, for solving large-scale Tikhonov minimization problems with a linear regularization operator of general form. The regularization parameter is determined by the discrepancy principle. Computed examples illustrate the performance of the Method.
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an Iterative Method for tikhonov regularization with a general linear regularization operator
CASA-report, 2010Co-Authors: Michiel E. Hochstenbach, Lothar ReichelAbstract:Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed problems with error-contaminated data. A regularization operator and a suitable value of a regularization parameter have to be chosen. This paper describes an Iterative Method, based on Golub-Kahan bidiagonalization, for solving large-scale Tikhonov minimization problems with a linear regularization operator of general form. The regularization parameter is determined by the discrepancy principle. Computed examples illustrate the performance of the Method. Key words. Discrete ill-posed problem, Iterative Method, Tikhonov regularization, general linear regularization operator, discrepancy principle.
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An Iterative Method with error estimators
Journal of Computational and Applied Mathematics, 2001Co-Authors: Daniela Calvetti, Lothar Reichel, Serena Morigi, Fiorella SgallariAbstract:Abstract Iterative Methods for the solution of linear systems of equations produce a sequence of approximate solutions. In many applications it is desirable to be able to compute estimates of the norm of the error in the approximate solutions generated and terminate the iterations when the estimates are sufficiently small. This paper presents a new Iterative Method based on the Lanczos process for the solution of linear systems of equations with a symmetric matrix. The Method is designed to allow the computation of estimates of the Euclidean norm of the error in the computed approximate solutions. These estimates are determined by evaluating certain Gauss, anti-Gauss, or Gauss–Radau quadrature rules.
Antti Hannukainen - One of the best experts on this subject based on the ideXlab platform.
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An Iterative Method for elliptic problems with rapidly oscillating coefficients
ESAIM: Mathematical Modelling and Numerical Analysis, 2021Co-Authors: Scott Armstrong, Antti Hannukainen, Tuomo Kuusi, Jean-christophe MourratAbstract:We introduce a new Iterative Method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid Method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid Methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our Method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the Method, with openly available source code.
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An Iterative Method for elliptic problems with rapidly oscillating coefficients
2018Co-Authors: Scott Armstrong, Antti Hannukainen, Tuomo Kuusi, Jean-christophe MourratAbstract:We introduce a new Iterative Method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid Method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid Methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our Method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the Method.
Tuomo Kuusi - One of the best experts on this subject based on the ideXlab platform.
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An Iterative Method for elliptic problems with rapidly oscillating coefficients
ESAIM: Mathematical Modelling and Numerical Analysis, 2021Co-Authors: Scott Armstrong, Antti Hannukainen, Tuomo Kuusi, Jean-christophe MourratAbstract:We introduce a new Iterative Method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid Method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid Methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our Method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the Method, with openly available source code.
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An Iterative Method for elliptic problems with rapidly oscillating coefficients
2018Co-Authors: Scott Armstrong, Antti Hannukainen, Tuomo Kuusi, Jean-christophe MourratAbstract:We introduce a new Iterative Method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid Method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid Methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our Method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the Method.
